LMFDB - Embedded newform 17.10.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,10,Mod(1,17)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("17.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	17.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$8.75560921479$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 2986x^{5} + 8252x^{4} + 2252056x^{3} - 10388768x^{2} - 243559296x - 675998208 $ x^7 - x^6 - 2986x^5 + 8252x^4 + 2252056x^3 - 10388768x^2 - 243559296*x - 675998208
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-4.12962$ of defining polynomial
Character	$\chi$	$=$	17.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.12962 q^{2} -254.074 q^{3} -494.946 q^{4} +151.544 q^{5} -1049.23 q^{6} +9407.97 q^{7} -4158.31 q^{8} +44870.8 q^{9} +O(q^{10})$	\(q+4.12962 q^{2} -254.074 q^{3} -494.946 q^{4} +151.544 q^{5} -1049.23 q^{6} +9407.97 q^{7} -4158.31 q^{8} +44870.8 q^{9} +625.818 q^{10} -56967.2 q^{11} +125753. q^{12} -60874.5 q^{13} +38851.3 q^{14} -38503.4 q^{15} +236240. q^{16} +83521.0 q^{17} +185299. q^{18} +1.00994e6 q^{19} -75006.0 q^{20} -2.39032e6 q^{21} -235253. q^{22} +1.35979e6 q^{23} +1.05652e6 q^{24} -1.93016e6 q^{25} -251388. q^{26} -6.39958e6 q^{27} -4.65644e6 q^{28} +3.12503e6 q^{29} -159004. q^{30} +2.97426e6 q^{31} +3.10463e6 q^{32} +1.44739e7 q^{33} +344910. q^{34} +1.42572e6 q^{35} -2.22086e7 q^{36} +681625. q^{37} +4.17068e6 q^{38} +1.54666e7 q^{39} -630165. q^{40} -4.09135e6 q^{41} -9.87113e6 q^{42} +1.00085e7 q^{43} +2.81957e7 q^{44} +6.79989e6 q^{45} +5.61542e6 q^{46} +2.54570e7 q^{47} -6.00226e7 q^{48} +4.81562e7 q^{49} -7.97082e6 q^{50} -2.12206e7 q^{51} +3.01296e7 q^{52} -3.14563e7 q^{53} -2.64278e7 q^{54} -8.63302e6 q^{55} -3.91212e7 q^{56} -2.56601e8 q^{57} +1.29052e7 q^{58} -9.03573e7 q^{59} +1.90571e7 q^{60} +9.87113e7 q^{61} +1.22826e7 q^{62} +4.22143e8 q^{63} -1.08134e8 q^{64} -9.22514e6 q^{65} +5.97717e7 q^{66} +1.32700e8 q^{67} -4.13384e7 q^{68} -3.45488e8 q^{69} +5.88767e6 q^{70} +4.18554e8 q^{71} -1.86587e8 q^{72} +4.80282e7 q^{73} +2.81485e6 q^{74} +4.90404e8 q^{75} -4.99868e8 q^{76} -5.35945e8 q^{77} +6.38714e7 q^{78} +3.49030e7 q^{79} +3.58007e7 q^{80} +7.42778e8 q^{81} -1.68957e7 q^{82} -2.05650e8 q^{83} +1.18308e9 q^{84} +1.26571e7 q^{85} +4.13311e7 q^{86} -7.93991e8 q^{87} +2.36887e8 q^{88} -2.03866e8 q^{89} +2.80810e7 q^{90} -5.72705e8 q^{91} -6.73023e8 q^{92} -7.55684e8 q^{93} +1.05128e8 q^{94} +1.53050e8 q^{95} -7.88808e8 q^{96} +1.24300e9 q^{97} +1.98867e8 q^{98} -2.55616e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9}+O(q^{10}) $ 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9	\( 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9} + 154226 q^{10} + 135536 q^{11} + 198160 q^{12} + 166122 q^{13} + 447252 q^{14} + 159048 q^{15} + 1463585 q^{16} + 584647 q^{17} + 149027 q^{18} + 777172 q^{19} - 917162 q^{20} - 3412104 q^{21} - 1222520 q^{22} + 1357764 q^{23} - 8487360 q^{24} + 1065785 q^{25} - 14379966 q^{26} - 4519064 q^{27} - 3328892 q^{28} + 967002 q^{29} - 12558992 q^{30} + 3546740 q^{31} + 4825461 q^{32} + 11928016 q^{33} - 83521 q^{34} - 530736 q^{35} + 4535009 q^{36} + 18296498 q^{37} - 49363020 q^{38} + 86306872 q^{39} + 127155062 q^{40} + 10285686 q^{41} + 14620416 q^{42} + 21913204 q^{43} + 96696624 q^{44} + 108916410 q^{45} - 151509484 q^{46} + 56639800 q^{47} - 201398496 q^{48} + 27010351 q^{49} - 261150303 q^{50} + 7349848 q^{51} - 156226378 q^{52} + 121813562 q^{53} - 93375344 q^{54} + 40793128 q^{55} - 196175436 q^{56} + 153612960 q^{57} - 236833910 q^{58} + 29222388 q^{59} - 628643488 q^{60} - 49915846 q^{61} - 73506556 q^{62} - 2185356 q^{63} + 317922057 q^{64} - 122633668 q^{65} - 624886144 q^{66} + 301863420 q^{67} + 199531669 q^{68} + 379683432 q^{69} + 966315960 q^{70} + 652473940 q^{71} + 655760385 q^{72} + 306656342 q^{73} + 249173874 q^{74} + 919071912 q^{75} + 128694700 q^{76} - 102442536 q^{77} + 323434416 q^{78} + 959147884 q^{79} - 692173602 q^{80} - 374486977 q^{81} + 1046441254 q^{82} - 1512945268 q^{83} - 481790592 q^{84} + 113755602 q^{85} - 164953236 q^{86} - 1612550856 q^{87} + 1132038848 q^{88} - 1971327114 q^{89} - 2284664662 q^{90} - 1061062864 q^{91} + 901186756 q^{92} - 798598936 q^{93} + 2534831232 q^{94} - 3249631512 q^{95} - 4442036640 q^{96} + 2006526254 q^{97} - 2170640009 q^{98} - 2579159272 q^{99}+O(q^{100}) \) 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9 + 154226 * q^10 + 135536 * q^11 + 198160 * q^12 + 166122 * q^13 + 447252 * q^14 + 159048 * q^15 + 1463585 * q^16 + 584647 * q^17 + 149027 * q^18 + 777172 * q^19 - 917162 * q^20 - 3412104 * q^21 - 1222520 * q^22 + 1357764 * q^23 - 8487360 * q^24 + 1065785 * q^25 - 14379966 * q^26 - 4519064 * q^27 - 3328892 * q^28 + 967002 * q^29 - 12558992 * q^30 + 3546740 * q^31 + 4825461 * q^32 + 11928016 * q^33 - 83521 * q^34 - 530736 * q^35 + 4535009 * q^36 + 18296498 * q^37 - 49363020 * q^38 + 86306872 * q^39 + 127155062 * q^40 + 10285686 * q^41 + 14620416 * q^42 + 21913204 * q^43 + 96696624 * q^44 + 108916410 * q^45 - 151509484 * q^46 + 56639800 * q^47 - 201398496 * q^48 + 27010351 * q^49 - 261150303 * q^50 + 7349848 * q^51 - 156226378 * q^52 + 121813562 * q^53 - 93375344 * q^54 + 40793128 * q^55 - 196175436 * q^56 + 153612960 * q^57 - 236833910 * q^58 + 29222388 * q^59 - 628643488 * q^60 - 49915846 * q^61 - 73506556 * q^62 - 2185356 * q^63 + 317922057 * q^64 - 122633668 * q^65 - 624886144 * q^66 + 301863420 * q^67 + 199531669 * q^68 + 379683432 * q^69 + 966315960 * q^70 + 652473940 * q^71 + 655760385 * q^72 + 306656342 * q^73 + 249173874 * q^74 + 919071912 * q^75 + 128694700 * q^76 - 102442536 * q^77 + 323434416 * q^78 + 959147884 * q^79 - 692173602 * q^80 - 374486977 * q^81 + 1046441254 * q^82 - 1512945268 * q^83 - 481790592 * q^84 + 113755602 * q^85 - 164953236 * q^86 - 1612550856 * q^87 + 1132038848 * q^88 - 1971327114 * q^89 - 2284664662 * q^90 - 1061062864 * q^91 + 901186756 * q^92 - 798598936 * q^93 + 2534831232 * q^94 - 3249631512 * q^95 - 4442036640 * q^96 + 2006526254 * q^97 - 2170640009 * q^98 - 2579159272 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	4.12962	0.182505	0.0912526	−	0.995828i	$-0.470913\pi$
$2$	4.12962	0.182505	0.0912526	+	0.995828i	$0.470913\pi$
$3$	−254.074	−1.81099	−0.905493	−	0.424360i	$-0.860499\pi$
$3$	−254.074	−1.81099	−0.905493	+	0.424360i	$0.860499\pi$
$4$	−494.946	−0.966692
$5$	151.544	0.108436	0.0542179	−	0.998529i	$-0.482733\pi$
$5$	151.544	0.108436	0.0542179	+	0.998529i	$0.482733\pi$
$6$	−1049.23	−0.330514
$7$	9407.97	1.48100	0.740499	−	0.672057i	$-0.234589\pi$
$7$	9407.97	1.48100	0.740499	+	0.672057i	$0.234589\pi$
$8$	−4158.31	−0.358931
$9$	44870.8	2.27967
$10$	625.818	0.0197901
$11$	−56967.2	−1.17316	−0.586581	−	0.809891i	$-0.699526\pi$
$11$	−56967.2	−1.17316	−0.586581	+	0.809891i	$0.699526\pi$
$12$	125753.	1.75067
$13$	−60874.5	−0.591140	−0.295570	−	0.955321i	$-0.595510\pi$
$13$	−60874.5	−0.591140	−0.295570	+	0.955321i	$0.595510\pi$
$14$	38851.3	0.270290
$15$	−38503.4	−0.196376
$16$	236240.	0.901185
$17$	83521.0	0.242536
$17$	83521.0	0.242536
$18$	185299.	0.416052
$19$	1.00994e6	1.77789	0.888947	−	0.458010i	$-0.151438\pi$
$19$	1.00994e6	1.77789	0.888947	+	0.458010i	$0.151438\pi$
$20$	−75006.0	−0.104824
$21$	−2.39032e6	−2.68207
$22$	−235253.	−0.214108
$23$	1.35979e6	1.01320	0.506602	−	0.862180i	$-0.330901\pi$
$23$	1.35979e6	1.01320	0.506602	+	0.862180i	$0.330901\pi$
$24$	1.05652e6	0.650020
$25$	−1.93016e6	−0.988242
$26$	−251388.	−0.107886
$27$	−6.39958e6	−2.31747
$28$	−4.65644e6	−1.43167
$29$	3.12503e6	0.820472	0.410236	−	0.911979i	$-0.365446\pi$
$29$	3.12503e6	0.820472	0.410236	+	0.911979i	$0.365446\pi$
$30$	−159004.	−0.0358396
$31$	2.97426e6	0.578431	0.289216	−	0.957264i	$-0.406606\pi$
$31$	2.97426e6	0.578431	0.289216	+	0.957264i	$0.406606\pi$
$32$	3.10463e6	0.523402
$33$	1.44739e7	2.12458
$34$	344910.	0.0442640
$35$	1.42572e6	0.160593
$36$	−2.22086e7	−2.20374
$37$	681625.	0.0597913	0.0298956	−	0.999553i	$-0.490483\pi$
$37$	681625.	0.0597913	0.0298956	+	0.999553i	$0.490483\pi$
$38$	4.17068e6	0.324475
$39$	1.54666e7	1.07055
$40$	−630165.	−0.0389210
$41$	−4.09135e6	−0.226120	−0.113060	−	0.993588i	$-0.536065\pi$
$41$	−4.09135e6	−0.226120	−0.113060	+	0.993588i	$0.536065\pi$
$42$	−9.87113e6	−0.489491
$43$	1.00085e7	0.446436	0.223218	−	0.974769i	$-0.428344\pi$
$43$	1.00085e7	0.446436	0.223218	+	0.974769i	$0.428344\pi$
$44$	2.81957e7	1.13409
$45$	6.79989e6	0.247198
$46$	5.61542e6	0.184915
$47$	2.54570e7	0.760970	0.380485	−	0.924787i	$-0.375757\pi$
$47$	2.54570e7	0.760970	0.380485	+	0.924787i	$0.375757\pi$
$48$	−6.00226e7	−1.63203
$49$	4.81562e7	1.19336
$50$	−7.97082e6	−0.180359
$51$	−2.12206e7	−0.439229
$52$	3.01296e7	0.571450
$53$	−3.14563e7	−0.547603	−0.273801	−	0.961786i	$-0.588281\pi$
$53$	−3.14563e7	−0.547603	−0.273801	+	0.961786i	$0.588281\pi$
$54$	−2.64278e7	−0.422951
$55$	−8.63302e6	−0.127213
$56$	−3.91212e7	−0.531577
$57$	−2.56601e8	−3.21974
$58$	1.29052e7	0.149740
$59$	−9.03573e7	−0.970798	−0.485399	−	0.874293i	$-0.661326\pi$
$59$	−9.03573e7	−0.970798	−0.485399	+	0.874293i	$0.661326\pi$
$60$	1.90571e7	0.189835
$61$	9.87113e7	0.912815	0.456408	−	0.889771i	$-0.349136\pi$
$61$	9.87113e7	0.912815	0.456408	+	0.889771i	$0.349136\pi$
$62$	1.22826e7	0.105567
$63$	4.22143e8	3.37619
$64$	−1.08134e8	−0.805661
$65$	−9.22514e6	−0.0641007
$66$	5.97717e7	0.387747
$67$	1.32700e8	0.804516	0.402258	−	0.915526i	$-0.368225\pi$
$67$	1.32700e8	0.804516	0.402258	+	0.915526i	$0.368225\pi$
$68$	−4.13384e7	−0.234457
$69$	−3.45488e8	−1.83490
$70$	5.88767e6	0.0293091
$71$	4.18554e8	1.95474	0.977369	−	0.211541i	$-0.0678482\pi$
$71$	4.18554e8	1.95474	0.977369	+	0.211541i	$0.0678482\pi$
$72$	−1.86587e8	−0.818246
$73$	4.80282e7	0.197944	0.0989721	−	0.995090i	$-0.468445\pi$
$73$	4.80282e7	0.197944	0.0989721	+	0.995090i	$0.468445\pi$
$74$	2.81485e6	0.0109122
$75$	4.90404e8	1.78969
$76$	−4.99868e8	−1.71868
$77$	−5.35945e8	−1.73745
$78$	6.38714e7	0.195380
$79$	3.49030e7	0.100819	0.0504093	−	0.998729i	$-0.483947\pi$
$79$	3.49030e7	0.100819	0.0504093	+	0.998729i	$0.483947\pi$
$80$	3.58007e7	0.0977207
$81$	7.42778e8	1.91724
$82$	−1.68957e7	−0.0412681
$83$	−2.05650e8	−0.475638	−0.237819	−	0.971309i	$-0.576433\pi$
$83$	−2.05650e8	−0.475638	−0.237819	+	0.971309i	$0.576433\pi$
$84$	1.18308e9	2.59273
$85$	1.26571e7	0.0262995
$86$	4.13311e7	0.0814769
$87$	−7.93991e8	−1.48586
$88$	2.36887e8	0.421084
$89$	−2.03866e8	−0.344422	−0.172211	−	0.985060i	$-0.555091\pi$
$89$	−2.03866e8	−0.344422	−0.172211	+	0.985060i	$0.555091\pi$
$90$	2.80810e7	0.0451150
$91$	−5.72705e8	−0.875477
$92$	−6.73023e8	−0.979456
$93$	−7.55684e8	−1.04753
$94$	1.05128e8	0.138881
$95$	1.53050e8	0.192787
$96$	−7.88808e8	−0.947875
$97$	1.24300e9	1.42560	0.712798	−	0.701369i	$-0.247427\pi$
$97$	1.24300e9	1.42560	0.712798	+	0.701369i	$0.247427\pi$
$98$	1.98867e8	0.217794
$99$	−2.55616e9	−2.67443
$100$	9.55325e8	0.955325
$101$	−2.02496e9	−1.93629	−0.968144	−	0.250395i	$-0.919440\pi$
$101$	−2.02496e9	−1.93629	−0.968144	+	0.250395i	$0.919440\pi$
$102$	−8.76328e7	−0.0801615
$103$	1.16276e9	1.01794	0.508970	−	0.860785i	$-0.330027\pi$
$103$	1.16276e9	1.01794	0.508970	+	0.860785i	$0.330027\pi$
$104$	2.53135e8	0.212179
$105$	−3.62238e8	−0.290832
$106$	−1.29902e8	−0.0999403
$107$	1.31593e9	0.970520	0.485260	−	0.874370i	$-0.338725\pi$
$107$	1.31593e9	0.970520	0.485260	+	0.874370i	$0.338725\pi$
$108$	3.16745e9	2.24028
$109$	−1.79000e8	−0.121460	−0.0607302	−	0.998154i	$-0.519343\pi$
$109$	−1.79000e8	−0.121460	−0.0607302	+	0.998154i	$0.519343\pi$
$110$	−3.56511e7	−0.0232170
$111$	−1.73184e8	−0.108281
$112$	2.22254e9	1.33465
$113$	2.53572e9	1.46301	0.731506	−	0.681835i	$-0.238818\pi$
$113$	2.53572e9	1.46301	0.731506	+	0.681835i	$0.238818\pi$
$114$	−1.05966e9	−0.587619
$115$	2.06068e8	0.109868
$116$	−1.54672e9	−0.793144
$117$	−2.73149e9	−1.34761
$118$	−3.73141e8	−0.177176
$119$	7.85763e8	0.359195
$120$	1.60109e8	0.0704854
$121$	8.87314e8	0.376308
$122$	4.07640e8	0.166593
$123$	1.03951e9	0.409500
$124$	−1.47210e9	−0.559165
$125$	−5.88487e8	−0.215597
$126$	1.74329e9	0.616172
$127$	4.05326e9	1.38257	0.691287	−	0.722581i	$-0.257044\pi$
$127$	4.05326e9	1.38257	0.691287	+	0.722581i	$0.257044\pi$
$128$	−2.03613e9	−0.670440
$129$	−2.54289e9	−0.808490
$130$	−3.80963e7	−0.0116987
$131$	−2.93543e9	−0.870865	−0.435432	−	0.900221i	$-0.643405\pi$
$131$	−2.93543e9	−0.870865	−0.435432	+	0.900221i	$0.643405\pi$
$132$	−7.16381e9	−2.05381
$133$	9.50151e9	2.63306
$134$	5.48001e8	0.146828
$135$	−9.69816e8	−0.251297
$136$	−3.47306e8	−0.0870536
$137$	−4.82610e9	−1.17045	−0.585226	−	0.810870i	$-0.698994\pi$
$137$	−4.82610e9	−1.17045	−0.585226	+	0.810870i	$0.698994\pi$
$138$	−1.42673e9	−0.334879
$139$	2.65630e9	0.603546	0.301773	−	0.953380i	$-0.402421\pi$
$139$	2.65630e9	0.603546	0.301773	+	0.953380i	$0.402421\pi$
$140$	−7.05653e8	−0.155244
$141$	−6.46798e9	−1.37811
$142$	1.72847e9	0.356750
$143$	3.46785e9	0.693502
$144$	1.06003e10	2.05441
$145$	4.73579e8	0.0889685
$146$	1.98338e8	0.0361259
$147$	−1.22353e10	−2.16115
$148$	−3.37368e8	−0.0577998
$149$	−2.85114e9	−0.473894	−0.236947	−	0.971523i	$-0.576147\pi$
$149$	−2.85114e9	−0.473894	−0.236947	+	0.971523i	$0.576147\pi$
$150$	2.02518e9	0.326628
$151$	−8.37259e9	−1.31058	−0.655290	−	0.755378i	$-0.727454\pi$
$151$	−8.37259e9	−1.31058	−0.655290	+	0.755378i	$0.727454\pi$
$152$	−4.19965e9	−0.638142
$153$	3.74766e9	0.552902
$154$	−2.21325e9	−0.317094
$155$	4.50731e8	0.0627227
$156$	−7.65516e9	−1.03489
$157$	8.37311e9	1.09986	0.549931	−	0.835210i	$-0.314654\pi$
$157$	8.37311e9	1.09986	0.549931	+	0.835210i	$0.314654\pi$
$158$	1.44136e8	0.0183999
$159$	7.99223e9	0.991702
$160$	4.70488e8	0.0567555
$161$	1.27929e10	1.50055
$162$	3.06739e9	0.349906
$163$	−2.12079e8	−0.0235317	−0.0117659	−	0.999931i	$-0.503745\pi$
$163$	−2.12079e8	−0.0235317	−0.0117659	+	0.999931i	$0.503745\pi$
$164$	2.02500e9	0.218588
$165$	2.19343e9	0.230381
$166$	−8.49256e8	−0.0868064
$167$	−9.27756e9	−0.923017	−0.461509	−	0.887136i	$-0.652692\pi$
$167$	−9.27756e9	−0.923017	−0.461509	+	0.887136i	$0.652692\pi$
$168$	9.93969e9	0.962678
$169$	−6.89880e9	−0.650554
$170$	5.22689e7	0.00479980
$171$	4.53170e10	4.05302
$172$	−4.95365e9	−0.431566
$173$	−1.29744e10	−1.10123	−0.550617	−	0.834758i	$-0.685608\pi$
$173$	−1.29744e10	−1.10123	−0.550617	+	0.834758i	$0.685608\pi$
$174$	−3.27888e9	−0.271178
$175$	−1.81589e10	−1.46358
$176$	−1.34579e10	−1.05724
$177$	2.29575e10	1.75810
$178$	−8.41890e8	−0.0628587
$179$	2.58172e10	1.87962	0.939812	−	0.341692i	$-0.111000\pi$
$179$	2.58172e10	1.87962	0.939812	+	0.341692i	$0.111000\pi$
$180$	−3.36558e9	−0.238965
$181$	2.61713e9	0.181248	0.0906238	−	0.995885i	$-0.471114\pi$
$181$	2.61713e9	0.181248	0.0906238	+	0.995885i	$0.471114\pi$
$182$	−2.36505e9	−0.159779
$183$	−2.50800e10	−1.65310
$184$	−5.65443e9	−0.363671
$185$	1.03296e8	0.00648352
$186$	−3.12069e9	−0.191180
$187$	−4.75796e9	−0.284533
$188$	−1.25999e10	−0.735623
$189$	−6.02070e10	−3.43217
$190$	6.32040e8	0.0351847
$191$	8.25575e8	0.0448855	0.0224428	−	0.999748i	$-0.492856\pi$
$191$	8.25575e8	0.0448855	0.0224428	+	0.999748i	$0.492856\pi$
$192$	2.74741e10	1.45904
$193$	1.88810e10	0.979530	0.489765	−	0.871855i	$-0.337083\pi$
$193$	1.88810e10	0.979530	0.489765	+	0.871855i	$0.337083\pi$
$194$	5.13310e9	0.260179
$195$	2.34387e9	0.116086
$196$	−2.38347e10	−1.15361
$197$	1.73273e10	0.819659	0.409829	−	0.912162i	$-0.365588\pi$
$197$	1.73273e10	0.819659	0.409829	+	0.912162i	$0.365588\pi$
$198$	−1.05560e10	−0.488096
$199$	2.14638e10	0.970216	0.485108	−	0.874454i	$-0.338780\pi$
$199$	2.14638e10	0.970216	0.485108	+	0.874454i	$0.338780\pi$
$200$	8.02619e9	0.354711
$201$	−3.37157e10	−1.45697
$202$	−8.36231e9	−0.353382
$203$	2.94002e10	1.21512
$204$	1.05030e10	0.424599
$205$	−6.20018e8	−0.0245195
$206$	4.80175e9	0.185779
$207$	6.10149e10	2.30977
$208$	−1.43810e10	−0.532726
$209$	−5.75336e10	−2.08576
$210$	−1.49591e9	−0.0530784
$211$	7.73227e9	0.268557	0.134278	−	0.990944i	$-0.457128\pi$
$211$	7.73227e9	0.268557	0.134278	+	0.990944i	$0.457128\pi$
$212$	1.55692e10	0.529363
$213$	−1.06344e11	−3.54001
$214$	5.43427e9	0.177125
$215$	1.51672e9	0.0484096
$216$	2.66114e10	0.831814
$217$	2.79818e10	0.856656
$218$	−7.39204e8	−0.0221672
$219$	−1.22027e10	−0.358475
$220$	4.27288e9	0.122975
$221$	−5.08430e9	−0.143372
$222$	−7.15182e8	−0.0197619
$223$	9.27651e9	0.251196	0.125598	−	0.992081i	$-0.459915\pi$
$223$	9.27651e9	0.251196	0.125598	+	0.992081i	$0.459915\pi$
$224$	2.92083e10	0.775158
$225$	−8.66078e10	−2.25287
$226$	1.04715e10	0.267007
$227$	−1.00921e10	−0.252270	−0.126135	−	0.992013i	$-0.540257\pi$
$227$	−1.00921e10	−0.252270	−0.126135	+	0.992013i	$0.540257\pi$
$228$	1.27004e11	3.11250
$229$	−2.70436e10	−0.649837	−0.324918	−	0.945742i	$-0.605337\pi$
$229$	−2.70436e10	−0.649837	−0.324918	+	0.945742i	$0.605337\pi$
$230$	8.50981e8	0.0200514
$231$	1.36170e11	3.14650
$232$	−1.29948e10	−0.294493
$233$	6.83620e10	1.51954	0.759771	−	0.650191i	$-0.225311\pi$
$233$	6.83620e10	1.51954	0.759771	+	0.650191i	$0.225311\pi$
$234$	−1.12800e10	−0.245945
$235$	3.85785e9	0.0825164
$236$	4.47220e10	0.938463
$237$	−8.86795e9	−0.182581
$238$	3.24490e9	0.0655549
$239$	−2.57344e10	−0.510179	−0.255090	−	0.966917i	$-0.582105\pi$
$239$	−2.57344e10	−0.510179	−0.255090	+	0.966917i	$0.582105\pi$
$240$	−9.09605e9	−0.176971
$241$	−1.97738e10	−0.377584	−0.188792	−	0.982017i	$-0.560457\pi$
$241$	−1.97738e10	−0.377584	−0.188792	+	0.982017i	$0.560457\pi$
$242$	3.66427e9	0.0686781
$243$	−6.27578e10	−1.15462
$244$	−4.88568e10	−0.882411
$245$	7.29777e9	0.129402
$246$	4.29277e9	0.0747359
$247$	−6.14798e10	−1.05098
$248$	−1.23679e10	−0.207617
$249$	5.22504e10	0.861375
$250$	−2.43023e9	−0.0393475
$251$	3.35205e10	0.533063	0.266532	−	0.963826i	$-0.414122\pi$
$251$	3.35205e10	0.533063	0.266532	+	0.963826i	$0.414122\pi$
$252$	−2.08938e11	−3.26374
$253$	−7.74635e10	−1.18865
$254$	1.67384e10	0.252327
$255$	−3.21584e9	−0.0476281
$256$	4.69562e10	0.683303
$257$	−9.22091e10	−1.31848	−0.659242	−	0.751931i	$-0.729123\pi$
$257$	−9.22091e10	−1.31848	−0.659242	+	0.751931i	$0.729123\pi$
$258$	−1.05012e10	−0.147554
$259$	6.41271e9	0.0885508
$260$	4.56595e9	0.0619656
$261$	1.40223e11	1.87041
$262$	−1.21222e10	−0.158937
$263$	1.83512e10	0.236518	0.118259	−	0.992983i	$-0.462269\pi$
$263$	1.83512e10	0.236518	0.118259	+	0.992983i	$0.462269\pi$
$264$	−6.01869e10	−0.762578
$265$	−4.76700e9	−0.0593798
$266$	3.92376e10	0.480546
$267$	5.17972e10	0.623743
$268$	−6.56795e10	−0.777719
$269$	−9.60172e10	−1.11806	−0.559029	−	0.829148i	$-0.688826\pi$
$269$	−9.60172e10	−1.11806	−0.559029	+	0.829148i	$0.688826\pi$
$270$	−4.00497e9	−0.0458630
$271$	−1.61081e11	−1.81419	−0.907097	−	0.420922i	$-0.861706\pi$
$271$	−1.61081e11	−1.81419	−0.907097	+	0.420922i	$0.861706\pi$
$272$	1.97310e10	0.218569
$273$	1.45510e11	1.58548
$274$	−1.99300e10	−0.213614
$275$	1.09956e11	1.15937
$276$	1.70998e11	1.77378
$277$	5.34317e10	0.545305	0.272653	−	0.962113i	$-0.412099\pi$
$277$	5.34317e10	0.545305	0.272653	+	0.962113i	$0.412099\pi$
$278$	1.09695e10	0.110150
$279$	1.33458e11	1.31863
$280$	−5.92857e9	−0.0576419
$281$	1.48954e11	1.42520	0.712599	−	0.701572i	$-0.247518\pi$
$281$	1.48954e11	1.42520	0.712599	+	0.701572i	$0.247518\pi$
$282$	−2.67103e10	−0.251511
$283$	−5.51543e10	−0.511140	−0.255570	−	0.966790i	$-0.582263\pi$
$283$	−5.51543e10	−0.511140	−0.255570	+	0.966790i	$0.582263\pi$
$284$	−2.07162e11	−1.88963
$285$	−3.88862e10	−0.349135
$286$	1.43209e10	0.126568
$287$	−3.84913e10	−0.334883
$288$	1.39307e11	1.19319
$289$	6.97576e9	0.0588235
$290$	1.95570e9	0.0162372
$291$	−3.15813e11	−2.58174
$292$	−2.37714e10	−0.191351
$293$	−1.58399e11	−1.25559	−0.627794	−	0.778379i	$-0.716042\pi$
$293$	−1.58399e11	−1.25559	−0.627794	+	0.778379i	$0.716042\pi$
$294$	−5.05270e10	−0.394421
$295$	−1.36931e10	−0.105269
$296$	−2.83441e9	−0.0214610
$297$	3.64566e11	2.71877
$298$	−1.17741e10	−0.0864880
$299$	−8.27766e10	−0.598945
$300$	−2.42724e11	−1.73008
$301$	9.41592e10	0.661171
$302$	−3.45756e10	−0.239188
$303$	5.14490e11	3.50659
$304$	2.38589e11	1.60221
$305$	1.49591e10	0.0989818
$306$	1.54764e10	0.100907
$307$	2.33754e11	1.50188	0.750942	−	0.660368i	$-0.229600\pi$
$307$	2.33754e11	1.50188	0.750942	+	0.660368i	$0.229600\pi$
$308$	2.65264e11	1.67958
$309$	−2.95427e11	−1.84347
$310$	1.86135e9	0.0114472
$311$	−2.24488e11	−1.36073	−0.680363	−	0.732875i	$-0.738178\pi$
$311$	−2.24488e11	−1.36073	−0.680363	+	0.732875i	$0.738178\pi$
$312$	−6.43150e10	−0.384253
$313$	−2.83464e10	−0.166935	−0.0834676	−	0.996510i	$-0.526599\pi$
$313$	−2.83464e10	−0.166935	−0.0834676	+	0.996510i	$0.526599\pi$
$314$	3.45777e10	0.200730
$315$	6.39731e10	0.366100
$316$	−1.72751e10	−0.0974604
$317$	−1.13413e11	−0.630807	−0.315404	−	0.948958i	$-0.602140\pi$
$317$	−1.13413e11	−0.630807	−0.315404	+	0.948958i	$0.602140\pi$
$318$	3.30049e10	0.180991
$319$	−1.78024e11	−0.962546
$320$	−1.63870e10	−0.0873626
$321$	−3.34343e11	−1.75760
$322$	5.28297e10	0.273859
$323$	8.43515e10	0.431203
$324$	−3.67635e11	−1.85338
$325$	1.17497e11	0.584189
$326$	−8.75807e8	−0.00429466
$327$	4.54794e10	0.219963
$328$	1.70131e10	0.0811616
$329$	2.39499e11	1.12699
$330$	9.05803e9	0.0420456
$331$	−4.08556e10	−0.187079	−0.0935397	−	0.995616i	$-0.529818\pi$
$331$	−4.08556e10	−0.187079	−0.0935397	+	0.995616i	$0.529818\pi$
$332$	1.01786e11	0.459796
$333$	3.05851e10	0.136305
$334$	−3.83128e10	−0.168455
$335$	2.01099e10	0.0872384
$336$	−5.64691e11	−2.41704
$337$	1.14143e11	0.482075	0.241037	−	0.970516i	$-0.422512\pi$
$337$	1.14143e11	0.482075	0.241037	+	0.970516i	$0.422512\pi$
$338$	−2.84894e10	−0.118729
$339$	−6.44261e11	−2.64949
$340$	−6.26457e9	−0.0254236
$341$	−1.69435e11	−0.678593
$342$	1.87142e11	0.739697
$343$	7.34065e10	0.286359
$344$	−4.16182e10	−0.160240
$345$	−5.23565e10	−0.198969
$346$	−5.35793e10	−0.200981
$347$	−1.30233e11	−0.482213	−0.241106	−	0.970499i	$-0.577510\pi$
$347$	−1.30233e11	−0.482213	−0.241106	+	0.970499i	$0.577510\pi$
$348$	3.92983e11	1.43637
$349$	1.52443e11	0.550039	0.275020	−	0.961439i	$-0.411316\pi$
$349$	1.52443e11	0.550039	0.275020	+	0.961439i	$0.411316\pi$
$350$	−7.49892e10	−0.267112
$351$	3.89571e11	1.36995
$352$	−1.76862e11	−0.614035
$353$	4.83570e11	1.65757	0.828787	−	0.559565i	$-0.189032\pi$
$353$	4.83570e11	1.65757	0.828787	+	0.559565i	$0.189032\pi$
$354$	9.48056e10	0.320863
$355$	6.34292e10	0.211964
$356$	1.00903e11	0.332950
$357$	−1.99642e11	−0.650497
$358$	1.06615e11	0.343041
$359$	−3.20450e11	−1.01820	−0.509102	−	0.860706i	$-0.670023\pi$
$359$	−3.20450e11	−1.01820	−0.509102	+	0.860706i	$0.670023\pi$
$360$	−2.82760e10	−0.0887272
$361$	6.97298e11	2.16091
$362$	1.08078e10	0.0330786
$363$	−2.25444e11	−0.681488
$364$	2.83458e11	0.846316
$365$	7.27836e9	0.0214642
$366$	−1.03571e11	−0.301699
$367$	−1.77614e11	−0.511070	−0.255535	−	0.966800i	$-0.582252\pi$
$367$	−1.77614e11	−0.511070	−0.255535	+	0.966800i	$0.582252\pi$
$368$	3.21237e11	0.913084
$369$	−1.83582e11	−0.515480
$370$	4.26573e8	0.00118328
$371$	−2.95939e11	−0.810999
$372$	3.74023e11	1.01264
$373$	4.80280e11	1.28471	0.642355	−	0.766407i	$-0.277958\pi$
$373$	4.80280e11	1.28471	0.642355	+	0.766407i	$0.277958\pi$
$374$	−1.96486e10	−0.0519288
$375$	1.49520e11	0.390443
$376$	−1.05858e11	−0.273136
$377$	−1.90235e11	−0.485014
$378$	−2.48632e11	−0.626389
$379$	3.81929e11	0.950837	0.475419	−	0.879760i	$-0.342297\pi$
$379$	3.81929e11	0.950837	0.475419	+	0.879760i	$0.342297\pi$
$380$	−7.57518e10	−0.186366
$381$	−1.02983e12	−2.50382
$382$	3.40931e9	0.00819184
$383$	3.63419e11	0.863004	0.431502	−	0.902112i	$-0.357984\pi$
$383$	3.63419e11	0.863004	0.431502	+	0.902112i	$0.357984\pi$
$384$	5.17327e11	1.21416
$385$	−8.12191e10	−0.188402
$386$	7.79714e10	0.178769
$387$	4.49088e11	1.01773
$388$	−6.15216e11	−1.37811
$389$	−6.51726e11	−1.44308	−0.721542	−	0.692370i	$-0.756566\pi$
$389$	−6.51726e11	−1.44308	−0.721542	+	0.692370i	$0.756566\pi$
$390$	9.67930e9	0.0211862
$391$	1.13571e11	0.245738
$392$	−2.00248e11	−0.428333
$393$	7.45818e11	1.57713
$394$	7.15552e10	0.149592
$395$	5.28932e9	0.0109323
$396$	1.26516e12	2.58535
$397$	2.04054e11	0.412276	0.206138	−	0.978523i	$-0.433910\pi$
$397$	2.04054e11	0.412276	0.206138	+	0.978523i	$0.433910\pi$
$398$	8.86375e10	0.177069
$399$	−2.41409e12	−4.76843
$400$	−4.55981e11	−0.890589
$401$	−2.48041e11	−0.479042	−0.239521	−	0.970891i	$-0.576990\pi$
$401$	−2.48041e11	−0.479042	−0.239521	+	0.970891i	$0.576990\pi$
$402$	−1.39233e11	−0.265904
$403$	−1.81057e11	−0.341934
$404$	1.00225e12	1.87179
$405$	1.12563e11	0.207897
$406$	1.21412e11	0.221765
$407$	−3.88303e10	−0.0701448
$408$	8.82415e10	0.157653
$409$	−2.59982e11	−0.459397	−0.229698	−	0.973262i	$-0.573774\pi$
$409$	−2.59982e11	−0.459397	−0.229698	+	0.973262i	$0.573774\pi$
$410$	−2.56044e9	−0.00447494
$411$	1.22619e12	2.11967
$412$	−5.75503e11	−0.984033
$413$	−8.50078e11	−1.43775
$414$	2.51968e11	0.421546
$415$	−3.11649e10	−0.0515762
$416$	−1.88993e11	−0.309404
$417$	−6.74898e11	−1.09301
$418$	−2.37592e11	−0.380661
$419$	−5.23470e11	−0.829714	−0.414857	−	0.909887i	$-0.636168\pi$
$419$	−5.23470e11	−0.829714	−0.414857	+	0.909887i	$0.636168\pi$
$420$	1.79288e11	0.281145
$421$	4.04503e11	0.627555	0.313778	−	0.949497i	$-0.398405\pi$
$421$	4.04503e11	0.627555	0.313778	+	0.949497i	$0.398405\pi$
$422$	3.19313e10	0.0490130
$423$	1.14228e12	1.73476
$424$	1.30805e11	0.196552
$425$	−1.61209e11	−0.239684
$426$	−4.39159e11	−0.646069
$427$	9.28673e11	1.35188
$428$	−6.51313e11	−0.938194
$429$	−8.81092e11	−1.25592
$430$	6.26347e9	0.00883501
$431$	−5.97189e11	−0.833612	−0.416806	−	0.908995i	$-0.636851\pi$
$431$	−5.97189e11	−0.833612	−0.416806	+	0.908995i	$0.636851\pi$
$432$	−1.51184e12	−2.08847
$433$	−8.45782e11	−1.15628	−0.578140	−	0.815938i	$-0.696221\pi$
$433$	−8.45782e11	−1.15628	−0.578140	+	0.815938i	$0.696221\pi$
$434$	1.15554e11	0.156344
$435$	−1.20324e11	−0.161121
$436$	8.85956e10	0.117415
$437$	1.37331e12	1.80137
$438$	−5.03926e10	−0.0654234
$439$	4.42347e11	0.568424	0.284212	−	0.958761i	$-0.408268\pi$
$439$	4.42347e11	0.568424	0.284212	+	0.958761i	$0.408268\pi$
$440$	3.58987e10	0.0456606
$441$	2.16081e12	2.72046
$442$	−2.09962e10	−0.0261662
$443$	−2.05741e11	−0.253807	−0.126903	−	0.991915i	$-0.540504\pi$
$443$	−2.05741e11	−0.253807	−0.126903	+	0.991915i	$0.540504\pi$
$444$	8.57165e10	0.104675
$445$	−3.08946e10	−0.0373476
$446$	3.83085e10	0.0458446
$447$	7.24403e11	0.858215
$448$	−1.01732e12	−1.19318
$449$	1.29191e12	1.50012	0.750059	−	0.661371i	$-0.230025\pi$
$449$	1.29191e12	1.50012	0.750059	+	0.661371i	$0.230025\pi$
$450$	−3.57657e11	−0.411160
$451$	2.33073e11	0.265275
$452$	−1.25504e12	−1.41428
$453$	2.12726e12	2.37344
$454$	−4.16766e10	−0.0460406
$455$	−8.67898e10	−0.0949330
$456$	1.06702e12	1.15567
$457$	−2.65686e11	−0.284935	−0.142467	−	0.989799i	$-0.545504\pi$
$457$	−2.65686e11	−0.284935	−0.142467	+	0.989799i	$0.545504\pi$
$458$	−1.11680e11	−0.118599
$459$	−5.34499e11	−0.562070
$460$	−1.01992e11	−0.106208
$461$	4.14119e11	0.427043	0.213521	−	0.976938i	$-0.431507\pi$
$461$	4.14119e11	0.427043	0.213521	+	0.976938i	$0.431507\pi$
$462$	5.62330e11	0.574252
$463$	5.26394e11	0.532349	0.266175	−	0.963925i	$-0.414240\pi$
$463$	5.26394e11	0.532349	0.266175	+	0.963925i	$0.414240\pi$
$464$	7.38259e11	0.739397
$465$	−1.14519e11	−0.113590
$466$	2.82309e11	0.277324
$467$	5.24754e11	0.510540	0.255270	−	0.966870i	$-0.417836\pi$
$467$	5.24754e11	0.510540	0.255270	+	0.966870i	$0.417836\pi$
$468$	1.35194e12	1.30272
$469$	1.24844e12	1.19149
$470$	1.59315e10	0.0150597
$471$	−2.12739e12	−1.99184
$472$	3.75733e11	0.348450
$473$	−5.70154e11	−0.523741
$474$	−3.66213e10	−0.0333220
$475$	−1.94935e12	−1.75699
$476$	−3.88910e11	−0.347231
$477$	−1.41147e12	−1.24836
$478$	−1.06273e11	−0.0931103
$479$	−6.90731e11	−0.599514	−0.299757	−	0.954016i	$-0.596906\pi$
$479$	−6.90731e11	−0.599514	−0.299757	+	0.954016i	$0.596906\pi$
$480$	−1.19539e11	−0.102784
$481$	−4.14936e10	−0.0353450
$482$	−8.16582e10	−0.0689109
$483$	−3.25034e12	−2.71748
$484$	−4.39173e11	−0.363774
$485$	1.88368e11	0.154586
$486$	−2.59166e11	−0.210724
$487$	5.21019e11	0.419733	0.209867	−	0.977730i	$-0.432697\pi$
$487$	5.21019e11	0.419733	0.209867	+	0.977730i	$0.432697\pi$
$488$	−4.10472e11	−0.327638
$489$	5.38839e10	0.0426157
$490$	3.01370e10	0.0236166
$491$	3.74675e11	0.290930	0.145465	−	0.989363i	$-0.453532\pi$
$491$	3.74675e11	0.290930	0.145465	+	0.989363i	$0.453532\pi$
$492$	−5.14500e11	−0.395861
$493$	2.61006e11	0.198994
$494$	−2.53888e11	−0.191810
$495$	−3.87371e11	−0.290003
$496$	7.02641e11	0.521274
$497$	3.93774e12	2.89496
$498$	2.15774e11	0.157205
$499$	−1.96144e12	−1.41619	−0.708096	−	0.706116i	$-0.750446\pi$
$499$	−1.96144e12	−1.41619	−0.708096	+	0.706116i	$0.750446\pi$
$500$	2.91269e11	0.208415
$501$	2.35719e12	1.67157
$502$	1.38427e11	0.0972868
$503$	7.20856e11	0.502103	0.251051	−	0.967974i	$-0.419224\pi$
$503$	7.20856e11	0.502103	0.251051	+	0.967974i	$0.419224\pi$
$504$	−1.75540e12	−1.21182
$505$	−3.06870e11	−0.209963
$506$	−3.19895e11	−0.216935
$507$	1.75281e12	1.17814
$508$	−2.00615e12	−1.33652
$509$	4.96970e11	0.328171	0.164085	−	0.986446i	$-0.447533\pi$
$509$	4.96970e11	0.328171	0.164085	+	0.986446i	$0.447533\pi$
$510$	−1.32802e10	−0.00869238
$511$	4.51847e11	0.293155
$512$	1.23641e12	0.795146
$513$	−6.46321e12	−4.12022
$514$	−3.80789e11	−0.240630
$515$	1.76209e11	0.110381
$516$	1.25860e12	0.781560
$517$	−1.45022e12	−0.892740
$518$	2.64820e10	0.0161610
$519$	3.29646e12	1.99432
$520$	3.83609e10	0.0230078
$521$	−7.85633e11	−0.467143	−0.233572	−	0.972340i	$-0.575041\pi$
$521$	−7.85633e11	−0.467143	−0.233572	+	0.972340i	$0.575041\pi$
$522$	5.79067e11	0.341359
$523$	−1.28047e12	−0.748363	−0.374182	−	0.927355i	$-0.622076\pi$
$523$	−1.28047e12	−0.748363	−0.374182	+	0.927355i	$0.622076\pi$
$524$	1.45288e12	0.841858
$525$	4.61371e12	2.65053
$526$	7.57835e10	0.0431657
$527$	2.48413e11	0.140290
$528$	3.41932e12	1.91464
$529$	4.78790e10	0.0265824
$530$	−1.96859e10	−0.0108371
$531$	−4.05440e12	−2.21310
$532$	−4.70274e12	−2.54535
$533$	2.49059e11	0.133669
$534$	2.13903e11	0.113836
$535$	1.99420e11	0.105239
$536$	−5.51808e11	−0.288766
$537$	−6.55950e12	−3.40397
$538$	−3.96515e11	−0.204051
$539$	−2.74332e12	−1.40000
$540$	4.80007e11	0.242927
$541$	2.82997e12	1.42035	0.710174	−	0.704026i	$-0.248616\pi$
$541$	2.82997e12	1.42035	0.710174	+	0.704026i	$0.248616\pi$
$542$	−6.65205e11	−0.331100
$543$	−6.64947e11	−0.328237
$544$	2.59302e11	0.126944
$545$	−2.71264e10	−0.0131707
$546$	6.00900e11	0.289358
$547$	3.65687e12	1.74649	0.873247	−	0.487278i	$-0.162010\pi$
$547$	3.65687e12	1.74649	0.873247	+	0.487278i	$0.162010\pi$
$548$	2.38866e12	1.13147
$549$	4.42926e12	2.08092
$550$	4.54076e11	0.211590
$551$	3.15611e12	1.45871
$552$	1.43665e12	0.658603
$553$	3.28366e11	0.149312
$554$	2.20652e11	0.0995210
$555$	−2.62449e10	−0.0117416
$556$	−1.31473e12	−0.583443
$557$	−8.41201e11	−0.370298	−0.185149	−	0.982710i	$-0.559277\pi$
$557$	−8.41201e11	−0.370298	−0.185149	+	0.982710i	$0.559277\pi$
$558$	5.51129e11	0.240658
$559$	−6.09260e11	−0.263906
$560$	3.36812e11	0.144724
$561$	1.20888e12	0.515286
$562$	6.15125e11	0.260106
$563$	2.93812e12	1.23249	0.616243	−	0.787556i	$-0.288654\pi$
$563$	2.93812e12	1.23249	0.616243	+	0.787556i	$0.288654\pi$
$564$	3.20130e12	1.33220
$565$	3.84272e11	0.158643
$566$	−2.27766e11	−0.0932858
$567$	6.98803e12	2.83943
$568$	−1.74047e12	−0.701617
$569$	−2.06188e12	−0.824627	−0.412313	−	0.911042i	$-0.635279\pi$
$569$	−2.06188e12	−0.824627	−0.412313	+	0.911042i	$0.635279\pi$
$570$	−1.60585e11	−0.0637190
$571$	−2.23269e12	−0.878955	−0.439477	−	0.898254i	$-0.644836\pi$
$571$	−2.23269e12	−0.878955	−0.439477	+	0.898254i	$0.644836\pi$
$572$	−1.71640e12	−0.670403
$573$	−2.09757e11	−0.0812871
$574$	−1.58954e11	−0.0611179
$575$	−2.62461e12	−1.00129
$576$	−4.85206e12	−1.83665
$577$	−9.94350e11	−0.373464	−0.186732	−	0.982411i	$-0.559790\pi$
$577$	−9.94350e11	−0.373464	−0.186732	+	0.982411i	$0.559790\pi$
$578$	2.88072e10	0.0107356
$579$	−4.79719e12	−1.77392
$580$	−2.34396e11	−0.0860052
$581$	−1.93475e12	−0.704420
$582$	−1.30419e12	−0.471180
$583$	1.79198e12	0.642427
$584$	−1.99716e11	−0.0710484
$585$	−4.13940e11	−0.146129
$586$	−6.54126e11	−0.229151
$587$	−4.22018e12	−1.46710	−0.733549	−	0.679636i	$-0.762138\pi$
$587$	−4.22018e12	−1.46710	−0.733549	+	0.679636i	$0.762138\pi$
$588$	6.05580e12	2.08917
$589$	3.00384e12	1.02839
$590$	−5.65472e10	−0.0192122
$591$	−4.40243e12	−1.48439
$592$	1.61027e11	0.0538830
$593$	−4.49622e12	−1.49314	−0.746571	−	0.665305i	$-0.768301\pi$
$593$	−4.49622e12	−1.49314	−0.746571	+	0.665305i	$0.768301\pi$
$594$	1.50552e12	0.496189
$595$	1.19077e11	0.0389496
$596$	1.41116e12	0.458109
$597$	−5.45341e12	−1.75705
$598$	−3.41836e11	−0.109311
$599$	1.61824e11	0.0513598	0.0256799	−	0.999670i	$-0.491825\pi$
$599$	1.61824e11	0.0513598	0.0256799	+	0.999670i	$0.491825\pi$
$600$	−2.03925e12	−0.642377
$601$	−3.79766e12	−1.18735	−0.593677	−	0.804703i	$-0.702324\pi$
$601$	−3.79766e12	−1.18735	−0.593677	+	0.804703i	$0.702324\pi$
$602$	3.88842e11	0.120667
$603$	5.95437e12	1.83403
$604$	4.14398e12	1.26693
$605$	1.34467e11	0.0408052
$606$	2.12465e12	0.639971
$607$	9.59183e11	0.286782	0.143391	−	0.989666i	$-0.454199\pi$
$607$	9.59183e11	0.286782	0.143391	+	0.989666i	$0.454199\pi$
$608$	3.13550e12	0.930554
$609$	−7.46984e12	−2.20056
$610$	6.17753e10	0.0180647
$611$	−1.54968e12	−0.449839
$612$	−1.85489e12	−0.534486
$613$	2.49059e12	0.712409	0.356205	−	0.934408i	$-0.384071\pi$
$613$	2.49059e12	0.712409	0.356205	+	0.934408i	$0.384071\pi$
$614$	9.65315e11	0.274102
$615$	1.57531e11	0.0444045
$616$	2.22862e12	0.623625
$617$	−1.31221e12	−0.364519	−0.182259	−	0.983250i	$-0.558341\pi$
$617$	−1.31221e12	−0.364519	−0.182259	+	0.983250i	$0.558341\pi$
$618$	−1.22000e12	−0.336444
$619$	6.10985e12	1.67272	0.836359	−	0.548182i	$-0.184680\pi$
$619$	6.10985e12	1.67272	0.836359	+	0.548182i	$0.184680\pi$
$620$	−2.23087e11	−0.0606335
$621$	−8.70209e12	−2.34807
$622$	−9.27049e11	−0.248340
$623$	−1.91797e12	−0.510088
$624$	3.65384e12	0.964760
$625$	3.68066e12	0.964863
$626$	−1.17060e11	−0.0304665
$627$	1.46178e13	3.77728
$628$	−4.14424e12	−1.06323
$629$	5.69300e10	0.0145015
$630$	2.64185e11	0.0668152
$631$	−2.63235e12	−0.661016	−0.330508	−	0.943803i	$-0.607220\pi$
$631$	−2.63235e12	−0.661016	−0.330508	+	0.943803i	$0.607220\pi$
$632$	−1.45137e11	−0.0361869
$633$	−1.96457e12	−0.486353
$634$	−4.68353e11	−0.115126
$635$	6.14247e11	0.149920
$636$	−3.95573e12	−0.958670
$637$	−2.93148e12	−0.705440
$638$	−7.35173e11	−0.175670
$639$	1.87808e13	4.45617
$640$	−3.08562e11	−0.0726997
$641$	4.56614e12	1.06829	0.534144	−	0.845394i	$-0.320634\pi$
$641$	4.56614e12	1.06829	0.534144	+	0.845394i	$0.320634\pi$
$642$	−1.38071e12	−0.320771
$643$	−6.83172e12	−1.57609	−0.788044	−	0.615618i	$-0.788906\pi$
$643$	−6.83172e12	−1.57609	−0.788044	+	0.615618i	$0.788906\pi$
$644$	−6.33178e12	−1.45057
$645$	−3.85359e11	−0.0876692
$646$	3.48340e11	0.0786967
$647$	−3.87609e12	−0.869609	−0.434805	−	0.900525i	$-0.643183\pi$
$647$	−3.87609e12	−0.869609	−0.434805	+	0.900525i	$0.643183\pi$
$648$	−3.08870e12	−0.688157
$649$	5.14740e12	1.13890
$650$	4.85220e11	0.106617
$651$	−7.10945e12	−1.55139
$652$	1.04968e11	0.0227479
$653$	5.89438e12	1.26861	0.634306	−	0.773082i	$-0.281286\pi$
$653$	5.89438e12	1.26861	0.634306	+	0.773082i	$0.281286\pi$
$654$	1.87813e11	0.0401444
$655$	−4.44846e11	−0.0944329
$656$	−9.66541e11	−0.203776
$657$	2.15506e12	0.451248
$658$	9.89039e11	0.205682
$659$	6.62732e12	1.36884	0.684421	−	0.729087i	$-0.260055\pi$
$659$	6.62732e12	1.36884	0.684421	+	0.729087i	$0.260055\pi$
$660$	−1.08563e12	−0.222707
$661$	−1.51309e12	−0.308288	−0.154144	−	0.988048i	$-0.549262\pi$
$661$	−1.51309e12	−0.308288	−0.154144	+	0.988048i	$0.549262\pi$
$662$	−1.68718e11	−0.0341429
$663$	1.29179e12	0.259646
$664$	8.55155e11	0.170722
$665$	1.43989e12	0.285518
$666$	1.26305e11	0.0248763
$667$	4.24939e12	0.831306
$668$	4.59190e12	0.892273
$669$	−2.35692e12	−0.454913
$670$	8.30461e10	0.0159215
$671$	−5.62331e12	−1.07088
$672$	−7.42108e12	−1.40380
$673$	−7.99861e10	−0.0150296	−0.00751479	−	0.999972i	$-0.502392\pi$
$673$	−7.99861e10	−0.0150296	−0.00751479	+	0.999972i	$0.502392\pi$
$674$	4.71367e11	0.0879811
$675$	1.23522e13	2.29022
$676$	3.41453e12	0.628885
$677$	−1.28946e12	−0.235917	−0.117958	−	0.993019i	$-0.537635\pi$
$677$	−1.28946e12	−0.235917	−0.117958	+	0.993019i	$0.537635\pi$
$678$	−2.66055e12	−0.483546
$679$	1.16941e13	2.11131
$680$	−5.26320e10	−0.00943973
$681$	2.56415e12	0.456858
$682$	−6.99704e11	−0.123847
$683$	−1.41260e12	−0.248386	−0.124193	−	0.992258i	$-0.539634\pi$
$683$	−1.41260e12	−0.248386	−0.124193	+	0.992258i	$0.539634\pi$
$684$	−2.24295e13	−3.91802
$685$	−7.31365e11	−0.126919
$686$	3.03141e11	0.0522620
$687$	6.87108e12	1.17685
$688$	2.36440e12	0.402321
$689$	1.91488e12	0.323710
$690$	−2.16213e11	−0.0363128
$691$	−2.52816e12	−0.421846	−0.210923	−	0.977503i	$-0.567647\pi$
$691$	−2.52816e12	−0.421846	−0.210923	+	0.977503i	$0.567647\pi$
$692$	6.42163e12	1.06455
$693$	−2.40483e13	−3.96082
$694$	−5.37813e11	−0.0880063
$695$	4.02546e11	0.0654460
$696$	3.30166e12	0.533323
$697$	−3.41713e11	−0.0548422
$698$	6.29532e11	0.100385
$699$	−1.73690e13	−2.75187
$700$	8.98767e12	1.41483
$701$	6.98644e12	1.09276	0.546380	−	0.837537i	$-0.316005\pi$
$701$	6.98644e12	1.09276	0.546380	+	0.837537i	$0.316005\pi$
$702$	1.60878e12	0.250023
$703$	6.88403e11	0.106303
$704$	6.16009e12	0.945171
$705$	−9.80181e11	−0.149436
$706$	1.99696e12	0.302516
$707$	−1.90507e13	−2.86764
$708$	−1.13627e13	−1.69954
$709$	−4.48848e12	−0.667100	−0.333550	−	0.942732i	$-0.608247\pi$
$709$	−4.48848e12	−0.667100	−0.333550	+	0.942732i	$0.608247\pi$
$710$	2.61938e11	0.0386844
$711$	1.56612e12	0.229833
$712$	8.47738e11	0.123624
$713$	4.04438e12	0.586069
$714$	−8.24446e11	−0.118719
$715$	5.25530e11	0.0752005
$716$	−1.27781e13	−1.81702
$717$	6.53844e12	0.923928
$718$	−1.32334e12	−0.185828
$719$	−7.44881e12	−1.03946	−0.519729	−	0.854331i	$-0.673967\pi$
$719$	−7.44881e12	−1.03946	−0.519729	+	0.854331i	$0.673967\pi$
$720$	1.60641e12	0.222771
$721$	1.09392e13	1.50757
$722$	2.87957e12	0.394376
$723$	5.02401e12	0.683799
$724$	−1.29534e12	−0.175211
$725$	−6.03181e12	−0.810825
$726$	−9.30997e11	−0.124375
$727$	3.94611e12	0.523920	0.261960	−	0.965079i	$-0.415631\pi$
$727$	3.94611e12	0.523920	0.261960	+	0.965079i	$0.415631\pi$
$728$	2.38148e12	0.314236
$729$	1.32507e12	0.173766
$730$	3.00569e10	0.00391734
$731$	8.35917e11	0.108277
$732$	1.24133e13	1.59803
$733$	8.83103e12	1.12991	0.564955	−	0.825122i	$-0.308894\pi$
$733$	8.83103e12	1.12991	0.564955	+	0.825122i	$0.308894\pi$
$734$	−7.33479e11	−0.0932729
$735$	−1.85418e12	−0.234346
$736$	4.22165e12	0.530313
$737$	−7.55956e12	−0.943828
$738$	−7.58124e11	−0.0940777
$739$	−6.70494e12	−0.826980	−0.413490	−	0.910509i	$-0.635690\pi$
$739$	−6.70494e12	−0.826980	−0.413490	+	0.910509i	$0.635690\pi$
$740$	−5.11260e10	−0.00626756
$741$	1.56204e13	1.90332
$742$	−1.22212e12	−0.148011
$743$	−8.35278e12	−1.00550	−0.502749	−	0.864432i	$-0.667678\pi$
$743$	−8.35278e12	−1.00550	−0.502749	+	0.864432i	$0.667678\pi$
$744$	3.14237e12	0.375992
$745$	−4.32073e11	−0.0513870
$746$	1.98338e12	0.234466
$747$	−9.22768e12	−1.08430
$748$	2.35493e12	0.275056
$749$	1.23802e13	1.43734
$750$	6.17459e11	0.0712578
$751$	−1.43369e13	−1.64465	−0.822327	−	0.569015i	$-0.807325\pi$
$751$	−1.43369e13	−1.64465	−0.822327	+	0.569015i	$0.807325\pi$
$752$	6.01398e12	0.685775
$753$	−8.51671e12	−0.965371
$754$	−7.85597e11	−0.0885175
$755$	−1.26881e12	−0.142114
$756$	2.97992e13	3.31785
$757$	−1.30485e13	−1.44421	−0.722105	−	0.691784i	$-0.756825\pi$
$757$	−1.30485e13	−1.44421	−0.722105	+	0.691784i	$0.756825\pi$
$758$	1.57722e12	0.173533
$759$	1.96815e13	2.15263
$760$	−6.36431e11	−0.0691974
$761$	−3.25303e10	−0.00351607	−0.00175804	−	0.999998i	$-0.500560\pi$
$761$	−3.25303e10	−0.00351607	−0.00175804	+	0.999998i	$0.500560\pi$
$762$	−4.25281e12	−0.456960
$763$	−1.68403e12	−0.179883
$764$	−4.08615e11	−0.0433905
$765$	5.67933e11	0.0599544
$766$	1.50078e12	0.157503
$767$	5.50045e12	0.573877
$768$	−1.19304e13	−1.23745
$769$	1.79023e13	1.84603	0.923016	−	0.384761i	$-0.125716\pi$
$769$	1.79023e13	1.84603	0.923016	+	0.384761i	$0.125716\pi$
$770$	−3.35404e11	−0.0343843
$771$	2.34280e13	2.38776
$772$	−9.34509e12	−0.946903
$773$	2.45846e12	0.247660	0.123830	−	0.992303i	$-0.460482\pi$
$773$	2.45846e12	0.247660	0.123830	+	0.992303i	$0.460482\pi$
$774$	1.85456e12	0.185741
$775$	−5.74080e12	−0.571630
$776$	−5.16875e12	−0.511691
$777$	−1.62930e12	−0.160364
$778$	−2.69138e12	−0.263370
$779$	−4.13203e12	−0.402017
$780$	−1.16009e12	−0.112219
$781$	−2.38438e13	−2.29322
$782$	4.69005e11	0.0448485
$783$	−1.99989e13	−1.90142
$784$	1.13764e13	1.07543
$785$	1.26889e12	0.119264
$786$	3.07994e12	0.287833
$787$	−1.50623e13	−1.39961	−0.699803	−	0.714336i	$-0.746729\pi$
$787$	−1.50623e13	−1.39961	−0.699803	+	0.714336i	$0.746729\pi$
$788$	−8.57609e12	−0.792358
$789$	−4.66257e12	−0.428331
$790$	2.18429e10	0.00199521
$791$	2.38559e13	2.16672
$792$	1.06293e13	0.959935
$793$	−6.00900e12	−0.539601
$794$	8.42666e11	0.0752425
$795$	1.21117e12	0.107536
$796$	−1.06234e13	−0.937900
$797$	−1.58318e12	−0.138985	−0.0694924	−	0.997582i	$-0.522138\pi$
$797$	−1.58318e12	−0.138985	−0.0694924	+	0.997582i	$0.522138\pi$
$798$	−9.96928e12	−0.870263
$799$	2.12620e12	0.184562
$800$	−5.99244e12	−0.517248
$801$	−9.14765e12	−0.785169
$802$	−1.02431e12	−0.0874276
$803$	−2.73603e12	−0.232221
$804$	1.66875e13	1.40844
$805$	1.93868e12	0.162714
$806$	−7.47695e11	−0.0624047
$807$	2.43955e13	2.02479
$808$	8.42039e12	0.694994
$809$	1.09269e13	0.896871	0.448435	−	0.893815i	$-0.351981\pi$
$809$	1.09269e13	0.896871	0.448435	+	0.893815i	$0.351981\pi$
$810$	4.64843e11	0.0379423
$811$	−1.40564e13	−1.14098	−0.570492	−	0.821303i	$-0.693247\pi$
$811$	−1.40564e13	−1.14098	−0.570492	+	0.821303i	$0.693247\pi$
$812$	−1.45515e13	−1.17464
$813$	4.09267e13	3.28548
$814$	−1.60354e11	−0.0128018
$815$	−3.21393e10	−0.00255168
$816$	−5.01315e12	−0.395826
$817$	1.01080e13	0.793716
$818$	−1.07363e12	−0.0838423
$819$	−2.56977e13	−1.99580
$820$	3.06875e11	0.0237028
$821$	−8.17487e12	−0.627967	−0.313983	−	0.949429i	$-0.601664\pi$
$821$	−8.17487e12	−0.627967	−0.313983	+	0.949429i	$0.601664\pi$
$822$	5.06369e12	0.386852
$823$	1.18003e13	0.896587	0.448294	−	0.893886i	$-0.352032\pi$
$823$	1.18003e13	0.896587	0.448294	+	0.893886i	$0.352032\pi$
$824$	−4.83510e12	−0.365370
$825$	−2.79370e13	−2.09960
$826$	−3.51050e12	−0.262397
$827$	1.45470e13	1.08143	0.540716	−	0.841205i	$-0.318153\pi$
$827$	1.45470e13	1.08143	0.540716	+	0.841205i	$0.318153\pi$
$828$	−3.01991e13	−2.23284
$829$	−1.06246e13	−0.781301	−0.390650	−	0.920539i	$-0.627750\pi$
$829$	−1.06246e13	−0.781301	−0.390650	+	0.920539i	$0.627750\pi$
$830$	−1.28699e11	−0.00941293
$831$	−1.35756e13	−0.987541
$832$	6.58260e12	0.476258
$833$	4.02205e12	0.289431
$834$	−2.78707e12	−0.199481
$835$	−1.40596e12	−0.100088
$836$	2.84761e13	2.01628
$837$	−1.90340e13	−1.34050
$838$	−2.16173e12	−0.151427
$839$	−5.78736e12	−0.403229	−0.201614	−	0.979465i	$-0.564619\pi$
$839$	−5.78736e12	−0.403229	−0.201614	+	0.979465i	$0.564619\pi$
$840$	1.50630e12	0.104389
$841$	−4.74131e12	−0.326826
$842$	1.67044e12	0.114532
$843$	−3.78455e13	−2.58101
$844$	−3.82706e12	−0.259612
$845$	−1.04547e12	−0.0705433
$846$	4.71717e12	0.316603
$847$	8.34782e12	0.557311
$848$	−7.43124e12	−0.493492
$849$	1.40133e13	0.925669
$850$	−6.65731e11	−0.0437435
$851$	9.26868e11	0.0605808
$852$	5.26345e13	3.42209
$853$	1.49513e13	0.966958	0.483479	−	0.875356i	$-0.339373\pi$
$853$	1.49513e13	0.966958	0.483479	+	0.875356i	$0.339373\pi$
$854$	3.83507e12	0.246725
$855$	6.86750e12	0.439492
$856$	−5.47202e12	−0.348350
$857$	−1.61752e13	−1.02432	−0.512159	−	0.858890i	$-0.671154\pi$
$857$	−1.61752e13	−1.02432	−0.512159	+	0.858890i	$0.671154\pi$
$858$	−3.63857e12	−0.229213
$859$	−2.12735e13	−1.33312	−0.666562	−	0.745450i	$-0.732235\pi$
$859$	−2.12735e13	−1.33312	−0.666562	+	0.745450i	$0.732235\pi$
$860$	−7.50694e11	−0.0467972
$861$	9.77964e12	0.606469
$862$	−2.46616e12	−0.152139
$863$	1.58563e13	0.973093	0.486547	−	0.873655i	$-0.338256\pi$
$863$	1.58563e13	0.973093	0.486547	+	0.873655i	$0.338256\pi$
$864$	−1.98684e13	−1.21297
$865$	−1.96619e12	−0.119413
$866$	−3.49276e12	−0.211027
$867$	−1.77236e12	−0.106529
$868$	−1.38495e13	−0.828122
$869$	−1.98832e12	−0.118276
$870$	−4.96894e11	−0.0294054
$871$	−8.07805e12	−0.475582
$872$	7.44339e11	0.0435960
$873$	5.57742e13	3.24990
$874$	5.67126e12	0.328759
$875$	−5.53647e12	−0.319298
$876$	6.03969e12	0.346534
$877$	−1.59980e13	−0.913203	−0.456601	−	0.889671i	$-0.650933\pi$
$877$	−1.59980e13	−0.913203	−0.456601	+	0.889671i	$0.650933\pi$
$878$	1.82672e12	0.103740
$879$	4.02451e13	2.27385
$880$	−2.03947e12	−0.114642
$881$	1.84519e13	1.03193	0.515963	−	0.856611i	$-0.327434\pi$
$881$	1.84519e13	1.03193	0.515963	+	0.856611i	$0.327434\pi$
$882$	8.92332e12	0.496498
$883$	2.67143e11	0.0147884	0.00739420	−	0.999973i	$-0.497646\pi$
$883$	2.67143e11	0.0147884	0.00739420	+	0.999973i	$0.497646\pi$
$884$	2.51645e12	0.138597
$885$	3.47906e12	0.190641
$886$	−8.49630e11	−0.0463210
$887$	2.38695e13	1.29475	0.647377	−	0.762170i	$-0.275866\pi$
$887$	2.38695e13	1.29475	0.647377	+	0.762170i	$0.275866\pi$
$888$	7.20150e11	0.0388655
$889$	3.81330e13	2.04759
$890$	−1.27583e11	−0.00681614
$891$	−4.23140e13	−2.24923
$892$	−4.59138e12	−0.242829
$893$	2.57102e13	1.35292
$894$	2.99151e12	0.156629
$895$	3.91244e12	0.203819
$896$	−1.91558e13	−0.992920
$897$	2.10314e13	1.08468
$898$	5.33512e12	0.273779
$899$	9.29467e12	0.474587
$900$	4.28662e13	2.17783
$901$	−2.62726e12	−0.132813
$902$	9.62501e11	0.0484141
$903$	−2.39235e13	−1.19737
$904$	−1.05443e13	−0.525121
$905$	3.96610e11	0.0196537
$906$	8.78478e12	0.433166
$907$	−2.77628e13	−1.36217	−0.681085	−	0.732205i	$-0.738492\pi$
$907$	−2.77628e13	−1.36217	−0.681085	+	0.732205i	$0.738492\pi$
$908$	4.99505e12	0.243867
$909$	−9.08615e13	−4.41410
$910$	−3.58409e11	−0.0173258
$911$	2.28307e13	1.09821	0.549106	−	0.835753i	$-0.314968\pi$
$911$	2.28307e13	1.09821	0.549106	+	0.835753i	$0.314968\pi$
$912$	−6.06194e13	−2.90158
$913$	1.17153e13	0.558001
$914$	−1.09718e12	−0.0520021
$915$	−3.80072e12	−0.179255
$916$	1.33851e13	0.628192
$917$	−2.76164e13	−1.28975
$918$	−2.20728e12	−0.102581
$919$	−5.88802e11	−0.0272301	−0.0136150	−	0.999907i	$-0.504334\pi$
$919$	−5.88802e11	−0.0272301	−0.0136150	+	0.999907i	$0.504334\pi$
$920$	−8.56892e11	−0.0394349
$921$	−5.93909e13	−2.71989
$922$	1.71015e12	0.0779375
$923$	−2.54792e13	−1.15552
$924$	−6.73968e13	−3.04170
$925$	−1.31565e12	−0.0590882
$926$	2.17381e12	0.0971565
$927$	5.21739e13	2.32057
$928$	9.70209e12	0.429437
$929$	3.31307e13	1.45935	0.729676	−	0.683793i	$-0.239671\pi$
$929$	3.31307e13	1.45935	0.729676	+	0.683793i	$0.239671\pi$
$930$	−4.72921e11	−0.0207307
$931$	4.86350e13	2.12166
$932$	−3.38355e13	−1.46893
$933$	5.70366e13	2.46426
$934$	2.16703e12	0.0931761
$935$	−7.21038e11	−0.0308536
$936$	1.13584e13	0.483698
$937$	−1.19627e13	−0.506993	−0.253496	−	0.967336i	$-0.581581\pi$
$937$	−1.19627e13	−0.506993	−0.253496	+	0.967336i	$0.581581\pi$
$938$	5.15558e12	0.217453
$939$	7.20208e12	0.302317
$940$	−1.90943e12	−0.0797679
$941$	−2.09786e13	−0.872213	−0.436106	−	0.899895i	$-0.643643\pi$
$941$	−2.09786e13	−0.872213	−0.436106	+	0.899895i	$0.643643\pi$
$942$	−8.78532e12	−0.363520
$943$	−5.56338e12	−0.229106
$944$	−2.13460e13	−0.874869
$945$	−9.12399e12	−0.372170
$946$	−2.35452e12	−0.0955855
$947$	2.72802e13	1.10223	0.551115	−	0.834429i	$-0.314203\pi$
$947$	2.72802e13	1.10223	0.551115	+	0.834429i	$0.314203\pi$
$948$	4.38916e12	0.176500
$949$	−2.92369e12	−0.117013
$950$	−8.05008e12	−0.320659
$951$	2.88154e13	1.14238
$952$	−3.26744e12	−0.128926
$953$	−1.60893e13	−0.631858	−0.315929	−	0.948783i	$-0.602316\pi$
$953$	−1.60893e13	−0.631858	−0.315929	+	0.948783i	$0.602316\pi$
$954$	−5.82883e12	−0.227831
$955$	1.25111e11	0.00486720
$956$	1.27371e13	0.493186
$957$	4.52315e13	1.74316
$958$	−2.85246e12	−0.109414
$959$	−4.54038e13	−1.73344
$960$	4.16353e12	0.158212
$961$	−1.75934e13	−0.665417
$962$	−1.71353e11	−0.00645065
$963$	5.90467e13	2.21247
$964$	9.78696e12	0.365007
$965$	2.86130e12	0.106216
$966$	−1.34227e13	−0.495955
$967$	−5.02741e13	−1.84895	−0.924475	−	0.381242i	$-0.875497\pi$
$967$	−5.02741e13	−1.84895	−0.924475	+	0.381242i	$0.875497\pi$
$968$	−3.68972e12	−0.135069
$969$	−2.14316e13	−0.780902
$970$	7.77888e11	0.0282127
$971$	3.00761e13	1.08576	0.542881	−	0.839810i	$-0.317333\pi$
$971$	3.00761e13	1.08576	0.542881	+	0.839810i	$0.317333\pi$
$972$	3.10618e13	1.11616
$973$	2.49904e13	0.893851
$974$	2.15161e12	0.0766035
$975$	−2.98531e13	−1.05796
$976$	2.33196e13	0.822615
$977$	−4.15719e13	−1.45974	−0.729868	−	0.683588i	$-0.760419\pi$
$977$	−4.15719e13	−1.45974	−0.729868	+	0.683588i	$0.760419\pi$
$978$	2.22520e11	0.00777758
$979$	1.16137e13	0.404062
$980$	−3.61200e12	−0.125092
$981$	−8.03190e12	−0.276890
$982$	1.54727e12	0.0530962
$983$	−3.65566e12	−0.124875	−0.0624375	−	0.998049i	$-0.519887\pi$
$983$	−3.65566e12	−0.124875	−0.0624375	+	0.998049i	$0.519887\pi$
$984$	−4.32259e12	−0.146983
$985$	2.62584e12	0.0888804
$986$	1.07786e12	0.0363174
$987$	−6.08505e13	−2.04097
$988$	3.04292e13	1.01598
$989$	1.36094e13	0.452331
$990$	−1.59969e12	−0.0529271
$991$	−5.35178e13	−1.76265	−0.881326	−	0.472509i	$-0.843348\pi$
$991$	−5.35178e13	−1.76265	−0.881326	+	0.472509i	$0.843348\pi$
$992$	9.23400e12	0.302752
$993$	1.03804e13	0.338798
$994$	1.62614e13	0.528346
$995$	3.25271e12	0.105206
$996$	−2.58611e13	−0.832684
$997$	6.71487e11	0.0215233	0.0107617	−	0.999942i	$-0.496574\pi$
$997$	6.71487e11	0.0215233	0.0107617	+	0.999942i	$0.496574\pi$
$998$	−8.09999e12	−0.258462
$999$	−4.36212e12	−0.138565

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.a.b.1.4	✓	7
3.2	odd	2		153.10.a.f.1.4		7
4.3	odd	2		272.10.a.g.1.7		7
17.16	even	2		289.10.a.b.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.b.1.4	✓	7	1.1	even	1	trivial
153.10.a.f.1.4		7	3.2	odd	2
272.10.a.g.1.7		7	4.3	odd	2
289.10.a.b.1.4		7	17.16	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)

\(f(q)\)	\(=\)	\(q+4.12962 q^{2} -254.074 q^{3} -494.946 q^{4} +151.544 q^{5} -1049.23 q^{6} +9407.97 q^{7} -4158.31 q^{8} +44870.8 q^{9} +O(q^{10})\)	\(q+4.12962 q^{2} -254.074 q^{3} -494.946 q^{4} +151.544 q^{5} -1049.23 q^{6} +9407.97 q^{7} -4158.31 q^{8} +44870.8 q^{9} +625.818 q^{10} -56967.2 q^{11} +125753. q^{12} -60874.5 q^{13} +38851.3 q^{14} -38503.4 q^{15} +236240. q^{16} +83521.0 q^{17} +185299. q^{18} +1.00994e6 q^{19} -75006.0 q^{20} -2.39032e6 q^{21} -235253. q^{22} +1.35979e6 q^{23} +1.05652e6 q^{24} -1.93016e6 q^{25} -251388. q^{26} -6.39958e6 q^{27} -4.65644e6 q^{28} +3.12503e6 q^{29} -159004. q^{30} +2.97426e6 q^{31} +3.10463e6 q^{32} +1.44739e7 q^{33} +344910. q^{34} +1.42572e6 q^{35} -2.22086e7 q^{36} +681625. q^{37} +4.17068e6 q^{38} +1.54666e7 q^{39} -630165. q^{40} -4.09135e6 q^{41} -9.87113e6 q^{42} +1.00085e7 q^{43} +2.81957e7 q^{44} +6.79989e6 q^{45} +5.61542e6 q^{46} +2.54570e7 q^{47} -6.00226e7 q^{48} +4.81562e7 q^{49} -7.97082e6 q^{50} -2.12206e7 q^{51} +3.01296e7 q^{52} -3.14563e7 q^{53} -2.64278e7 q^{54} -8.63302e6 q^{55} -3.91212e7 q^{56} -2.56601e8 q^{57} +1.29052e7 q^{58} -9.03573e7 q^{59} +1.90571e7 q^{60} +9.87113e7 q^{61} +1.22826e7 q^{62} +4.22143e8 q^{63} -1.08134e8 q^{64} -9.22514e6 q^{65} +5.97717e7 q^{66} +1.32700e8 q^{67} -4.13384e7 q^{68} -3.45488e8 q^{69} +5.88767e6 q^{70} +4.18554e8 q^{71} -1.86587e8 q^{72} +4.80282e7 q^{73} +2.81485e6 q^{74} +4.90404e8 q^{75} -4.99868e8 q^{76} -5.35945e8 q^{77} +6.38714e7 q^{78} +3.49030e7 q^{79} +3.58007e7 q^{80} +7.42778e8 q^{81} -1.68957e7 q^{82} -2.05650e8 q^{83} +1.18308e9 q^{84} +1.26571e7 q^{85} +4.13311e7 q^{86} -7.93991e8 q^{87} +2.36887e8 q^{88} -2.03866e8 q^{89} +2.80810e7 q^{90} -5.72705e8 q^{91} -6.73023e8 q^{92} -7.55684e8 q^{93} +1.05128e8 q^{94} +1.53050e8 q^{95} -7.88808e8 q^{96} +1.24300e9 q^{97} +1.98867e8 q^{98} -2.55616e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9}+O(q^{10}) \) 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9	\( 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9} + 154226 q^{10} + 135536 q^{11} + 198160 q^{12} + 166122 q^{13} + 447252 q^{14} + 159048 q^{15} + 1463585 q^{16} + 584647 q^{17} + 149027 q^{18} + 777172 q^{19} - 917162 q^{20} - 3412104 q^{21} - 1222520 q^{22} + 1357764 q^{23} - 8487360 q^{24} + 1065785 q^{25} - 14379966 q^{26} - 4519064 q^{27} - 3328892 q^{28} + 967002 q^{29} - 12558992 q^{30} + 3546740 q^{31} + 4825461 q^{32} + 11928016 q^{33} - 83521 q^{34} - 530736 q^{35} + 4535009 q^{36} + 18296498 q^{37} - 49363020 q^{38} + 86306872 q^{39} + 127155062 q^{40} + 10285686 q^{41} + 14620416 q^{42} + 21913204 q^{43} + 96696624 q^{44} + 108916410 q^{45} - 151509484 q^{46} + 56639800 q^{47} - 201398496 q^{48} + 27010351 q^{49} - 261150303 q^{50} + 7349848 q^{51} - 156226378 q^{52} + 121813562 q^{53} - 93375344 q^{54} + 40793128 q^{55} - 196175436 q^{56} + 153612960 q^{57} - 236833910 q^{58} + 29222388 q^{59} - 628643488 q^{60} - 49915846 q^{61} - 73506556 q^{62} - 2185356 q^{63} + 317922057 q^{64} - 122633668 q^{65} - 624886144 q^{66} + 301863420 q^{67} + 199531669 q^{68} + 379683432 q^{69} + 966315960 q^{70} + 652473940 q^{71} + 655760385 q^{72} + 306656342 q^{73} + 249173874 q^{74} + 919071912 q^{75} + 128694700 q^{76} - 102442536 q^{77} + 323434416 q^{78} + 959147884 q^{79} - 692173602 q^{80} - 374486977 q^{81} + 1046441254 q^{82} - 1512945268 q^{83} - 481790592 q^{84} + 113755602 q^{85} - 164953236 q^{86} - 1612550856 q^{87} + 1132038848 q^{88} - 1971327114 q^{89} - 2284664662 q^{90} - 1061062864 q^{91} + 901186756 q^{92} - 798598936 q^{93} + 2534831232 q^{94} - 3249631512 q^{95} - 4442036640 q^{96} + 2006526254 q^{97} - 2170640009 q^{98} - 2579159272 q^{99}+O(q^{100}) \) 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9 + 154226 * q^10 + 135536 * q^11 + 198160 * q^12 + 166122 * q^13 + 447252 * q^14 + 159048 * q^15 + 1463585 * q^16 + 584647 * q^17 + 149027 * q^18 + 777172 * q^19 - 917162 * q^20 - 3412104 * q^21 - 1222520 * q^22 + 1357764 * q^23 - 8487360 * q^24 + 1065785 * q^25 - 14379966 * q^26 - 4519064 * q^27 - 3328892 * q^28 + 967002 * q^29 - 12558992 * q^30 + 3546740 * q^31 + 4825461 * q^32 + 11928016 * q^33 - 83521 * q^34 - 530736 * q^35 + 4535009 * q^36 + 18296498 * q^37 - 49363020 * q^38 + 86306872 * q^39 + 127155062 * q^40 + 10285686 * q^41 + 14620416 * q^42 + 21913204 * q^43 + 96696624 * q^44 + 108916410 * q^45 - 151509484 * q^46 + 56639800 * q^47 - 201398496 * q^48 + 27010351 * q^49 - 261150303 * q^50 + 7349848 * q^51 - 156226378 * q^52 + 121813562 * q^53 - 93375344 * q^54 + 40793128 * q^55 - 196175436 * q^56 + 153612960 * q^57 - 236833910 * q^58 + 29222388 * q^59 - 628643488 * q^60 - 49915846 * q^61 - 73506556 * q^62 - 2185356 * q^63 + 317922057 * q^64 - 122633668 * q^65 - 624886144 * q^66 + 301863420 * q^67 + 199531669 * q^68 + 379683432 * q^69 + 966315960 * q^70 + 652473940 * q^71 + 655760385 * q^72 + 306656342 * q^73 + 249173874 * q^74 + 919071912 * q^75 + 128694700 * q^76 - 102442536 * q^77 + 323434416 * q^78 + 959147884 * q^79 - 692173602 * q^80 - 374486977 * q^81 + 1046441254 * q^82 - 1512945268 * q^83 - 481790592 * q^84 + 113755602 * q^85 - 164953236 * q^86 - 1612550856 * q^87 + 1132038848 * q^88 - 1971327114 * q^89 - 2284664662 * q^90 - 1061062864 * q^91 + 901186756 * q^92 - 798598936 * q^93 + 2534831232 * q^94 - 3249631512 * q^95 - 4442036640 * q^96 + 2006526254 * q^97 - 2170640009 * q^98 - 2579159272 * q^99

Introduction

L-functions

Modular forms

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